They said in a statement it was wrong that players had to sell their medals -- like Stiles did -- to provide for their family when the PFA has "tens of millions of pounds available".
They also questioned how so many former players could be struggling to survive when the Premier League "receives £3 billion ($4 billion) a year".
Ex-Manchester United and England midfielder Stiles died in October, aged 78. He had dementia and prostate cancer.
Stiles, part of the United side that became the first English club to lift the European Cup in 1968, is the fifth member of England's World Cup-winning squad to have been diagnosed with dementia.
Previous research has shown ex-footballers are three-and-a-half times more likely to die of dementia than the general population.
In a statement paying tribute to their pride of "what he (Stiles) achieved but more importantly, the man he was", the family said: "There is a need for urgent action.
"These older players have largely been forgotten and many are in ill health, like dad.
"How can it be that these players are left needing help when their own union has tens of millions of pounds available today?
"How can it be that these players (are) struggling when the Premier League receives £3bn a year?
"The modern player will never need the help required by the older lads.
"How can it be right that some of the heroes of 1966 had to sell their medals to provide for the families?
"These older players are dying like my dad. Many don't have medals to sell."
The family said the PFA should urgently address the issue of players suffering from dementia.
"It is right, of course to seek to identify the cause of dementia in older players," they said.
"But in truth the cause is irrelevant to the older players.
"Whatever the cause they need help now. I hope dad's death is the catalyst for this scandal to be addressed."
The English Football Association (FA) issued a statement saying all interested parties in football should combine to get to the bottom of the dementia issue.
"Collaboration across football's governing bodies is key in order to better understand this important issue collectively," they said.
"We firmly believe that all areas of football should come together for this meaningful cause."